Investment Science: Yearly, monthly and Continuous compounding

Write it in your head, the formula we learnt in school, the growth in compound interest given by

Where

P = Principal (or Present value)

FV = Growth in compounding (or Future value)
r = Yearly interest rate
m = Number of compounding periods per year (say monthly, quarterly or yearly)
n = number of years (n * m then gives the number of compounding periods for "n" years)

Though this is a simple equation, but the foundations of investment science lies in this simple, yet powerful formula.

For example, if you invest $1000 (P) in a bank for 10 years (n) with an interest rate 5% (r) compounded yearly (m = 1), then the growth in compound interest will be

FV = 1000 * [ (1 + 0.05 / 1) ^ (10 * 1) ] = $1628.89463

That's quite easy, but the fun comes when m > 1 or the number of times the interest compounded per year is > 1, the interest can be compounded every 6 months (m = 2), 3 months (m = 3) or monthly (m = 12).

Assuming that the interest is compounded monthly, then

FV = 1000 * [ (1 + 0.05 / 12) ^ (10 * 12) ] = $1647.0095

The returns in the monthly compounding is little better than that of yearly compounding, in case of continuous compounding, where the number of compounding intervals m -> Infinity, then we have

The below excel spreadsheet (I have used openoffice, but it can be imported as excel) can be used to calculate the compound interest based on the Present value (P), number of years (n), number of compounding intervals (m) and interest rate (r).

1. Compound interest spreadsheet

Question: Try increasing the number of times the interest is compounded yearly (m) in the spreadsheet, note the difference between the growth with that of the growth using continuous compounding.